I have the same problem, and it really makes me feel like I have no (or maybe just the dullest possible) personality. It's like my brain shuts off during conversation, I wrack my brains out trying to think of something to say and end up with nothing. It's like a mental war for me.
I strongly believe it's due to anxiety. Are you the same way around people close to you (Mother, father, siblings, etc)? I am able to hold a conversation with people close to me, which validates my suspicion that is just anxiety related.